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The image shows a question involving a quadrilateral ABCD, where \(E\) is the midpoint of \(AD\), and you're asked to solve two parts:

1. **(i)** Find the area (in cm²) of quadrilateral \(ABCE\).
2. **(ii)** Given \(x = 4\), determine the value of \(y\).

### Dimensions Provided:
- \(AB = 2x \, \text{cm}\)
- \(AD = 5y \, \text{cm}\)
- \(CE\) is a diagonal, splitting the quadrilateral into two triangles.

#### Solving Part (i): 
To find the area of quadrilateral \(ABCE\), we can break it into two triangles: \(\triangle ABE\) and \(\triangle CBE\).

1. **Area of \(\triangle ABE\):**
   - The base is \(AB = 2x \, \text{cm}\).
   - The height is half of \(AD\), since \(E\) is the midpoint, so the height is \(\frac{5y}{2}\).

   The area of a triangle is given by:
   \[
   \text{Area of } \triangle ABE = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 2x \times \frac{5y}{2} = \frac{5xy}{2}
   \]

2. **Area of \(\triangle CBE\):**
   - This triangle shares the base \(AB = 2x\) and has the same height as \(\triangle ABE\).

   The area of this triangle is the same as \(\triangle ABE\), so:
   \[
   \text{Area of } \triangle CBE = \frac{5xy}{2}
   \]

3. **Total Area of Quadrilateral \(ABCE\):**
   \[
   \text{Total area} = \text{Area of } \triangle ABE + \text{Area of } \triangle CBE = \frac{5xy}{2} + \frac{5xy}{2} = 5xy \, \text{cm}^2
   \]

### Solving Part (ii): 
Given \(x = 4\), substitute into the area formula from part (i):
\[
\text{Area} = 5xy = 5(4)(y) = 20y \, \text{cm}^2
\]
If the area is provided, we could solve for \(y\).

Let me know if any further clarification is needed or if you want to provide the total area for \(y\).

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Here are 5 related questions:
1. How do you calculate the area of other shapes, like trapezoids or parallelograms?
2. What happens to the area if the dimensions of the rectangle are doubled?
3. Can you calculate the area of a triangle without knowing the height?
4. How would you calculate the perimeter of quadrilateral \(ABCE\)?
5. How does knowing \(E\) is the midpoint help simplify the calculations?

**Tip**: When working with midpoints, they often simplify problems by dividing lengths into equal halves.

Find the area (in cm²) of quadrilateral ABCE, and determine the value of y given x = 4.

Learn how to calculate the area of quadrilateral ABCE and solve for y when given x = 4. This problem involves geometry concepts like triangle area and midpoint theorem, suitable for students in Grades 9-10.

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